Robust Stabilization Over Communication Channels in the Presence of Unstructured Uncertainty

This technical note is concerned with the problem of controlling plants over communication channels, where the plant is subject to two types of unstructured uncertainty: additive uncertainty and stable coprime factor uncertainty. Necessary lower bounds on the rate of transmission (or channel capacity) C, for robust stabilization, are computed explicitly. In particular, it is shown that the lower bound in the additive uncertainty case corresponds to a fixed point of a particular function. In the stable coprime factor uncertainty case, the derivation relies on linear fractional transformation concepts. The results are important in determining the minimum channel capacity needed in order to stabilize plants subject to unstructured uncertainty over communication channels. For instance, the bounds obtained can be used to analyze the effect of uncertainty on the channel capacity. An illustrative example is provided.